This tutorial illustrates the core visualization utilities available in Ax.
import numpy as np
from ax.service.ax_client import AxClient
from ax.modelbridge.cross_validation import cross_validate
from ax.plot.contour import interact_contour
from ax.plot.diagnostic import interact_cross_validation
from ax.plot.scatter import(
interact_fitted,
plot_objective_vs_constraints,
tile_fitted,
)
from ax.plot.slice import plot_slice
from ax.utils.measurement.synthetic_functions import hartmann6
from ax.utils.notebook.plotting import render, init_notebook_plotting
init_notebook_plotting()
[INFO 05-13 05:35:00] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.
The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials
noise_sd = 0.1
param_names = [f"x{i+1}" for i in range(6)] # x1, x2, ..., x6
def noisy_hartmann_evaluation_function(parameterization):
x = np.array([parameterization.get(p_name) for p_name in param_names])
noise1, noise2 = np.random.normal(0, noise_sd, 2)
return {
"hartmann6": (hartmann6(x) + noise1, noise_sd),
"l2norm": (np.sqrt((x ** 2).sum()) + noise2, noise_sd)
}
ax_client = AxClient()
ax_client.create_experiment(
name="test_visualizations",
parameters=[
{
"name": p_name,
"type": "range",
"bounds": [0.0, 1.0],
}
for p_name in param_names
],
objective_name="hartmann6",
minimize=True,
outcome_constraints=["l2norm <= 1.25"]
)
[INFO 05-13 05:35:00] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 05-13 05:35:00] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[]).
[INFO 05-13 05:35:00] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.
[INFO 05-13 05:35:00] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 12 trials, GPEI for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.
for i in range(20):
parameters, trial_index = ax_client.get_next_trial()
# Local evaluation here can be replaced with deployment to external system.
ax_client.complete_trial(trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters))
[INFO 05-13 05:35:00] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.236509, 'x2': 0.881197, 'x3': 0.698507, 'x4': 0.922798, 'x5': 0.79916, 'x6': 0.351307}.
[INFO 05-13 05:35:00] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.124966, 0.1), 'l2norm': (1.664388, 0.1)}.
[INFO 05-13 05:35:00] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.17379, 'x2': 0.54472, 'x3': 0.044239, 'x4': 0.71351, 'x5': 0.291599, 'x6': 0.034596}.
[INFO 05-13 05:35:00] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.469371, 0.1), 'l2norm': (0.947326, 0.1)}.
[INFO 05-13 05:35:00] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.636089, 'x2': 0.441124, 'x3': 0.053539, 'x4': 0.032731, 'x5': 0.068825, 'x6': 0.314666}.
[INFO 05-13 05:35:00] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.078803, 0.1), 'l2norm': (0.892689, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.193891, 'x2': 0.705078, 'x3': 0.006604, 'x4': 0.235821, 'x5': 0.408127, 'x6': 0.343244}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.36209, 0.1), 'l2norm': (1.033464, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.342499, 'x2': 0.175218, 'x3': 0.827574, 'x4': 0.740629, 'x5': 0.219015, 'x6': 0.707682}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.318906, 0.1), 'l2norm': (1.333733, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.900444, 'x2': 0.7835, 'x3': 0.828076, 'x4': 0.281337, 'x5': 0.99861, 'x6': 0.363833}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.033644, 0.1), 'l2norm': (1.961336, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.453861, 'x2': 0.935882, 'x3': 0.371277, 'x4': 0.54802, 'x5': 0.324155, 'x6': 0.318094}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-1.020501, 0.1), 'l2norm': (1.279691, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.50031, 'x2': 0.702992, 'x3': 0.925486, 'x4': 0.089295, 'x5': 0.797831, 'x6': 0.034127}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.183324, 0.1), 'l2norm': (1.468428, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.921787, 'x2': 0.453485, 'x3': 0.841085, 'x4': 0.956517, 'x5': 0.852205, 'x6': 0.346687}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.044691, 0.1), 'l2norm': (1.849519, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.374315, 'x2': 0.577414, 'x3': 0.354058, 'x4': 0.067542, 'x5': 0.518179, 'x6': 0.467735}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.294645, 0.1), 'l2norm': (0.925857, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.914367, 'x2': 0.887504, 'x3': 0.35478, 'x4': 0.474316, 'x5': 0.736865, 'x6': 0.701477}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.044126, 0.1), 'l2norm': (1.774946, 0.1)}.
[INFO 05-13 05:35:01] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.628361, 'x2': 0.226653, 'x3': 0.270114, 'x4': 0.865842, 'x5': 0.806319, 'x6': 0.04077}.
[INFO 05-13 05:35:01] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (0.119222, 0.1), 'l2norm': (1.312229, 0.1)}.
[INFO 05-13 05:35:18] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.392441, 'x2': 0.815288, 'x3': 0.282738, 'x4': 0.498484, 'x5': 0.308346, 'x6': 0.288122}.
[INFO 05-13 05:35:18] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.25087, 0.1), 'l2norm': (1.354446, 0.1)}.
[INFO 05-13 05:35:32] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.334624, 'x2': 0.698089, 'x3': 0.192619, 'x4': 0.451888, 'x5': 0.310989, 'x6': 0.279012}.
[INFO 05-13 05:35:32] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.074539, 0.1), 'l2norm': (0.929441, 0.1)}.
[INFO 05-13 05:35:57] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.373735, 'x2': 0.730116, 'x3': 0.255263, 'x4': 0.508164, 'x5': 0.295373, 'x6': 0.281838}.
[INFO 05-13 05:35:57] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.162464, 0.1), 'l2norm': (0.899655, 0.1)}.
[INFO 05-13 05:36:11] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.365164, 'x2': 0.744265, 'x3': 0.359239, 'x4': 0.475844, 'x5': 0.27925, 'x6': 0.258836}.
[INFO 05-13 05:36:11] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.255628, 0.1), 'l2norm': (1.11367, 0.1)}.
[INFO 05-13 05:36:24] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.373629, 'x2': 0.773338, 'x3': 0.312478, 'x4': 0.494807, 'x5': 0.216115, 'x6': 0.314863}.
[INFO 05-13 05:36:24] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.117914, 0.1), 'l2norm': (0.981834, 0.1)}.
[INFO 05-13 05:36:38] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.41134, 'x2': 0.780215, 'x3': 0.300662, 'x4': 0.494707, 'x5': 0.267422, 'x6': 0.168892}.
[INFO 05-13 05:36:38] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.20551, 0.1), 'l2norm': (1.118509, 0.1)}.
[INFO 05-13 05:37:11] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.43802, 'x2': 0.796158, 'x3': 0.273384, 'x4': 0.499939, 'x5': 0.217935, 'x6': 0.141416}.
[INFO 05-13 05:37:11] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.499101, 0.1), 'l2norm': (1.057117, 0.1)}.
[INFO 05-13 05:37:20] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.461225, 'x2': 0.822104, 'x3': 0.267566, 'x4': 0.483417, 'x5': 0.183655, 'x6': 0.105876}.
[INFO 05-13 05:37:20] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.550588, 0.1), 'l2norm': (1.238985, 0.1)}.
The plot below shows the response surface for hartmann6 metric as a function of the x1, x2 parameters.
The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them.
# this could alternately be done with `ax.plot.contour.plot_contour`
render(ax_client.get_contour_plot(param_x="x1", param_y="x2", metric_name='hartmann6'))
[INFO 05-13 05:37:20] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.
The plot below allows toggling between different pairs of parameters to view the contours.
model = ax_client.generation_strategy.model
render(interact_contour(model=model, metric_name='hartmann6'))
This plot illustrates the tradeoffs achievable for 2 different metrics. The plot takes the x-axis metric as input (usually the objective) and allows toggling among all other metrics for the y-axis.
This is useful to get a sense of the pareto frontier (i.e. what is the best objective value achievable for different bounds on the constraint)
render(plot_objective_vs_constraints(model, 'hartmann6', rel=False))
CV plots are useful to check how well the model predictions calibrate against the actual measurements. If all points are close to the dashed line, then the model is a good predictor of the real data.
cv_results = cross_validate(model)
render(interact_cross_validation(cv_results))
Slice plots show the metric outcome as a function of one parameter while fixing the others. They serve a similar function as contour plots.
render(plot_slice(model, "x2", "hartmann6"))
Tile plots are useful for viewing the effect of each arm.
render(interact_fitted(model, rel=False))
Total runtime of script: 2 minutes, 41.06 seconds.